PDE - Yet another

This is my third question regarding PDE solvable as ODE and I am still confused because the book I am following (Advanced Engineering Mathematics by Erwin Kreyszig) has only two very elementary examples where as I find the exercise problems to be very difficult, especially in their approach.

Currently I am having problem in Q5 of Problem Set 12.1.

How do I approach this one. I write in differential form but then I do not know how to handle the part. Can someone please explain the solutiion to this one.

And please can I be provided with some links to online examples for PDEs solvable as ODEs ?

This is my third question regarding PDE solvable as ODE and I am still confused because the book I am following (Advanced Engineering Mathematics by Erwin Kreyszig) has only two very elementary examples where as I find the exercise problems to be very difficult, especially in their approach.

Currently I am having problem in Q5 of Problem Set 12.1.

How do I approach this one. I write in differential form but then I do not know how to handle the part. Can someone please explain the solutiion to this one.

And please can I be provided with some links to online examples for PDEs solvable as ODEs ?

Not sure on links to PDEs that can be solved as ODEs but I'll comment on the one you have here. You'll notice that your PDE has no x derivative so x is treated as a constant in your PDE. This problem is now like the following ODE

It's linear and can be solved using an integrating factor. Remember, put back the x( ) and with the constant of integration, it's a fucntion of integration.

A perhaps daft question to tag on the end here, but i thought the integrating factor method would only work for "proper" derivatives, not partial derivatives? I don't know where ive got this idea from, perhaps someone could clarify?

A perhaps daft question to tag on the end here, but i thought the integrating factor method would only work for "proper" derivatives, not partial derivatives? I don't know where ive got this idea from, perhaps someone could clarify?

The key thing here is the absence of the derivative. So the integrating factor for